Electrical frequency changer



Feb. 19 1942 J. M. MANLEY ELECTRICAL FREQUENCY CHANGER Filed Sept. 1'7, 1940 2 Sheets-Sheet 1 fl ARCTAIV 11/12 71/;

zm I INVENTOR J. M. MANL Er R BY NW ATTORNEY Feb. 10, 1942. J. M. MANLEY 2,272,246

' ELECTRICAL FREQUENCY CHANGER Filed Sept. 17, 1940 2 Shets-Sheet 2 FIG 10 FIG.

FIG. 13 Mk V FIG. /5

60 m 4 KC.

FIL TER QOUTPU T lNl/EN TOR I J. M. MANL El.

Patented Feb. 10,1942

, ELEC'IRICAL FREQUENCX QHANGEE Jack M. Manley, East 0range, N. 1., assignor to Bell Telephone laboratories, Incorporated, New York, N. Y., a corporation of New York Application September 17, 1940, Serial No; 357,115 6 Claims. (C1. 1'l2281) This invention relates to frequenc changing circuits and more particularly to means for ob taining a frequency other than that of a base irequency source.

The invention makes use of the well-known non-linear properties of magnetic coils and its object is to provide a reliable seli storting, self-' maintaining subfrequency generator calling for no special shock producing device to initiate the generation of sold suhfrequencies.

The invention will be better understood. by

reference to the following specification in which the limiting conditions for self-stoning ere set forth end by reference to the occomponyine; drawings inwhic'n:

Fig. l shows so simple representative circuit in= eluding s non linesr magnetic element;

Fig. 2 is represents-two of e typiccl magnetitetion curve for the non-lines? element;

Figs. 3 to 7 are curves explanatory of one man-- nor of operation oi my generator;

Figs. s oncl 9 are curves enplenotory of onother moms? of: operetion 02 any generator;

Figs. it to is are electricel networks which may he used connection with such. e circuit as that of Fig. i; and I Figs. 16 end i? ere circuits showing special epplicotions' oi my invention.

The possibility of existence in fen-roman neticolly coupled circuits of oscillations which ore not cool harmonics of the applied frequency is well known in the est. Circuits illustrsting this are disclosed in such patents us those to Follou, 1,633,4tl, June 21, W27; Heegner, 1,656,195, Jenuory 1?, 21.92%; Stoclzer, 2,088,620, August 3, will; end Kelli, 2,112,533, March 2Q, 1938. l

A classification oi such oscillations may be given as: (i) submultiples or sushi-colonies oi the applied wave, (2) even hermonics of the one pliezi wove, (3) rational iroctions, for which the ratio of frequencies of the generated wove and iii the applied wove is expressed by s, rotionsl from tion m/n, where neither m not n is unity, and (c) incommensurobles for which the frequency of oscillation is incommensurohle with the on= plied frequency.

it is well known that the open circuit voltage across on unbiased magnetic coil which is meg netized by e sinusoidal current contoins only oucl hormonics oi the magnetizing wove, where the exciting wove itseli is considered as one hon monic. It is also well known that if a sinusoidal voltage is spelled to the magnetic coil, the resulting current consists only of odd hormonics netisotion or l co 0: the applied wave. It follows then that the open circuit voltage referred to does not contain frequencies which come under the above iour classes and the question arises what special conditions must be fulfilleol in order to start the oscillations o1 non-odd harmonics. The analysis of the conditions existing is given in this specification and forms the basis for my invention.

In this analysis it is assumed that there are present a. few sinusoidal components 01 current through the coil or voltage across the coil and the conditions which must necessorily exist are then derived.

Referring to Fig. i there is shown o source of sinusoidal voitcge E1. of ireouency f1, current from which flows through c. non=lineor magnetic coil in. in the supply circuit there is included on inductance L1. and condenser .01 ior tuning pumoses as eirnloinecl hereinafter. Across the terminal of the coil L0 is connected o network Z, the pestle r cherccteriotics oi? which will be ciiscnssecl hereinoiter. In considering this circult it will he first assumed thot the current tlnougli the coil Lo consists oi only two sinusoiclsl componen'w. Under these conditions it is terms that oil the non-coo harmonic oscnlctions recited shove, except those oi? clues l, son he mointeineti under conditions, only the even. harmonics can he sting.

G1 the two sinusoidal comsonents o1 cur= rents the coil, one is the spoiled cor rent of J cuuency h, the other the generated oscillotien oi Ii. ioirly close o pronimstion, ignoring reels, to the uncles consideration silence in 2' end con be represent-eat very closely orctongent iunction o the Zoom where 1 the In go-let: is forc o is o constant ii= pencils upon the dimensions oncl piroperties oi the non-limes coil, Que makes use of the voltage circuitel equation thot the vectoiiol sum oi the components voltege across the coil and voltoge drop in the external circuit at the corresponding frequency must be eero at each frequency. Becouse oi its non-linens nro'oerties it is well lmown thet the voltoge across the new but that surable, I find that the above voltageequations for the circuit cannot be satisfied unless the resistance of Z at f: is zero and there are no losses in the magnetic coil. Ii, however, the ratio of ,1 and 1: can be expressed by a rational number, then some of the combination frequencies mh-nfz will coincide with f2. The phase of the voltage across the non-linear coil, due to this modulation product is such that a component of this voltage is opposite to the voltage drop in the resistance of Z at f2. sible to satisfy the voltage equations of the circuit in this case even though R2 (the resistance of Z) and the losses in the non-linear coil are greater than zero, provided R2 and the losses are small enough. Because the voltage generated across the non-linear coil neutralizes part or all of the drop in the external resistance it may be said that the non-linear coil has a negative resistance at f2. It may be noted that this negative resistance has the characteristics of the series type of negative resistance since any tendency toward oscillation can be stopped by increasing R2.

The relation between Z and P2 (the amplitude of the In component of magnetizing force) as determined by the voltage circuit equations for a typical case, are shown in Fig. 3. P: is plotted against R2 for several values of X2, wher X: is the reactance of Z at f: and must be negative. The phase of the fa component varies from point to point. From these curves of Fig. 3 it is seen that R2 must be less than a certain value Rim. Also it is seen that R2m varies with X2. Ran is largest for that value of X2 which approximately neutralizes the effective reactance of the nonlinear coil Lo for the particular values of P1 and P2 involved (P1 being the amplitude of the f1 component of magnetizing force). Whatever X2 may be, R2111 is proportional to 1121-0, 11: being 2112 and Lo the effective value of the non-linear inductance. For example, in the case of the 1/3 subharmonic, I find that the largest value of Rzm/pzLu is about one-half. Since P: is not zero for R2=R2m, P2 will suddenly drop to zero as R: increases and reaches R2111. The ratio of R212: to i zLo decreases as the order of subharmonic increases. Throughout this specification, the expression effective reactance oi. the non-linear coil (paLo) at some frequency 1: is used to designate the ratio of amplitudes Vii/Ia, where Va is the amplitude of the sinusoidal voltage component at frequency is across the coil in quandrature to the sinusoidal current component I]. through the coil at frequency fl.-

Variations of the amplitude P1 of the wave have two principal effects. First, the effective value of inductance Lo decreases with increase of P1, and hence R2m decreases with increase of P1 thus decreasing the range of R: over which oscillations can exist. Second, because of the variation of L with P1 the tuning of L0 with m is changed. This has the same effect as varying X1 and causes a change to another curve as on Fig. 3. If the variation of P1 is large enough the range over which oscillation is possible will be exceeded,'

and thus there are upper and lower limits for P1 other conditions remaining the same.

In order then tomaintain the oscillations at frequency I: it is necessary only that th inipedance Z be a simple resonant circuit with negative reactance of such magnitude that the effective inductance L0 is approximately nullified by it at b. tion of the network Z a simple anti-resonance at Consequently, it is pos- It may be desirable to include as a por-' f1 to prevent Z from shunting L0 to an appreciable extent at h.

The considerations above relate primarily to the steady state conditions which exist if once arrived at. It has already been mentioned, however, that one of the purposes of this invention is to provide a circuit which is self-starting and it is, therefore, desirable to consider the stability of the circuit under the conditions given above.

To this end it may be noted on reference to Fig. 3 that for each pair of values of R: and X2, there are two possible values of P2. Both values of P: satisfy the circuital equations, but I find that only those values lying on the upper branch of the curv (solid line) are stable and hence physically realizable. This fact has a connection with the question of starting. In the considerations above and the curves of Fig. 3 it was assumed that P: was constant with respect to time. If, however, we allow P: to vary slowly as a function of time (i. e. slow-with respect to the applied frequency) before the expressions for current are inserted in the differential equations, one attains results which depend not only on the amplitude P: but on th time derivative of amplitude dP2 /dt. I find under a given set of circumstances, this derivative turns out to be posi-- tive, in which case any disturbance, no matter how small, in the amplitude P2 will cause this amplitude to increase. If the derivative is negative, any disturbanc will cause the amplitude to decrease. In non-linear circuit problems this derivative is a function of the amplitude P2. This function is plotted in Fig. 5 for the case for which the stationary state solution is as shown in Fig. 3.- This plot is for constant values of R2 and X: corresponding to the vertical position which intersects the unstable branch of Fig. 4 at P==Pu and the stable branch at P2=P2s. For a stationary state, the derivative cZPfi/dt is zero. If the derivative is positive and the amplitude increases, then a value of P2 will be reached for which dPfi/dt is zero and thereafter negative. Thus the increase is stopped and a stable value of P: is reached. It is now seen from Fig. 5 why the lower branch of the stationary state curve is unstable and the upper branch is stable. Any small change in P2 that reduces it from P211 causes P: to decrease further until Pz=0, while any change that increases P2 from P211 causes P1: to be increased further until P28 is reached. Just the reverse is true for P2,. Any small change in either direction causes Pa to return to Pu. Thus P2; is a stable'stationary solution. P2=0 is also a stable solution.

It is now possible to draw certain conclusions as to the question of starting. First. since P2=U is a stable condition, the oscillations will not arise spontaneously, i. e. from the very small disturbances that are always present in any circuit. Second, any initial value of P: less than Pam will die away if there is no externally connected electromotive forc of frequency f: to maintain it. Third, any initial value of P2 between P211 and P2. will build up to Pile. Hence in order to start the oscillation which has a steady state curve like those of Fig. 3 it is necessary to have an initial amplitude of P2 greater than the value Pm corresponding to the particular values of R: and X: and P1 involved.

Suppose that no oscillation is present, 1. e., P: is zero and that R2, X2 and P1 have values such that for the corresponding curve of Fig. 3, Ha is less than R2m- Now let an external generator at frequency f2; having zero impedance and variable voltage, be connected'in series with Z. If the voltage of this generator is gradually increased from zero a current of frequency is will now, and

as long as the amplitude oi the magnetizing force corresponding to this current is less than P211 this current will beunder the control oi the external generator. That is, the current will increase or 1 decrease as the voltage is increased or decreased and would die away entirely ii the generator is removed. But if the voltage is increased until P: passes P2u,. then the oscillation is unstable and no longer under the control of the generator and will build up to a value near Pal. If now the external generator is removed, P2 does not die away but assumes the value P20. Experimentally determined curves of the form of Fig. 6 confirm these conclusions.

Steady state curves like those 01 Fig. 3 are obtained for classes i and 3 above, 1. e., subharmonics and rational fraction-a1 products, when two sinusoidal components of current are allowed to flow. Consequently subharmonic and rational fracional oscillations are not self-starting under these conditions. in the case of even harmonics a different kind of curve from those of Fig. 3 is obtained. As shown in Fig. 7 the lower branch does not appear as in Fig. 3. In this case I flnd that P2=0 is unstable when R: is less than R2111.

Hence this class of oscillation can arise spontaneously under the proper conditions of R2 andXz.

These results may be used to explain the starting action characteristics of some forms of subharmonic generators commonly used. These have but one degree of freedom besides that at the applied frequency and so conform to the assumptions made above. a relay switch to short-circuit a coil temporarily or some other means of applying a shock to the circuit is required for starting. The magnitude of the electrlcal transient resulting from such a shock depends on the phase of the applied wave at the time of shock. Since the time or application or the shock usually has no dete connection with the phase oi the applied wave, the magnitude oi the electrical transient will not necessarily be the same each time the shock is applied. The magnitude of the transient must be greater than a certain threshold value in order for starting to occur and hence the oscillation may or may not arise depending on whether or not the transient exceeds a certain threshold.

} A more general and more interesting case is that in which an additional sinusoidal component is allowed to flow. In that case I find that any of the four classes of non-odd harmonic oscillations referred to above can exist and can be sell-starting when the proper conditions are satisfied.

To consider this, let the impedance Z of M8. 1 be so arranged that the circuit has two degrees of freedom so that two sinusoidal components annulment, i. e., precise tuning for these irequencies is not necessary, as will be pointed out hereinafter. A certain amount of departure from such tuning is permissible within limits which will be specified. Besides this condition I also find that the total resistances at both f2 and is of the circuit mesh formed by Z and Lo must be less than a certain quantity which is a proportional to the magnitude of, the reactance pzLo. These two conditions turn out to be so connected that oscillations may arise when the reactance of Z is detuned from the above most favorable condition, provided the resistance is reduced from theabove maximum value by the proper amount. The exact relation (derived on the basis of the arctangent function as given for Fig. 2) which must be satisfied in order that oscillations f2 and ,1: shall arise spontaneously is 1 2 (X2 i- I 2 o) @H- ai'P3 o) Spc oPa o where R2 and R3 are the resistances of Z at 7: and f3 and & and K3 are the reactances of Z at hand is and where b is a parameter depending only on the magnetic characteristic of the dill coil and the amplitude Pi and is always less than unity, approaching unity as P1 becomes very large. v

It will be observed that the first factor on the left-hand side of the expression is the impedance Z2 of the circuit at f: and the second factor is the impedance Z: for the circuit at fa. On the right-hand side of the expression it will be observed min is the reactance X2 of the coil at J: and pain is the reactance X3 of the coil at is. Since b is less than unitythe expression above may be put in the more condensed form At first sight it might appear that since Z2 includes K2 the above expression would not be possible but it is to be observed that in Equation 2 the quantity Xz-i-pafio may be quite small, even approaching zero. Under this special condition Equation 2 would reduce to A curve for this case of three sinusoidal com-' ponents and corresponding to the curves of Fig. 3

is shown in d. it will be seen that the eszero, we have tor the intersection point for R2 till besides the applied current are allowed to flow through the non=linear coil. In this case oscillations at two separate frequencies are produced and these have a definite relation to the applied frequency. If h is again the applied frequency and is and J: are the generated frequencies, the relation is 2mf1=is+fs where m is an integer. an analysis shows that the most favorable conditions for starting the oscillations occur when the reactance of the impedance Z nullifles the efiectlve inductive reactance Lo 0! the non-linear I cell at the two frequencies 1: and 1:. Complete investigation shows that both time derivatives" dPzldt and dPs /dt are positive for infinitesimal values of Pa and in when the condition of Equation 2 is satisfied. Thus in this condition the situation of sore amplitude ior P2 and P3 is unstable when the resistance is to the left of the intersection point oi the steady state curve of- 3 corresponds to the other parameters or rivatives of amplitude become positive, the condition of zero values for amplitudes P2 and P3 is unstable and the oscillations at f: and is will automatically build up, having been started off by the small disturbances present in any circuit. This set of conditions is shown in Fig. 9 in which a sudden building up of oscillations is shown when R: is lowered to R20. For further decrease of R: the amplitude of oscillation will increase slowly. Increase of resistance above R20 will still permit the oscillations to continue until Ra reaches the value Rem whereupon the oscillations die down very quickly.

It is possible to trace the reasons for the starting performance of this circuit to the modulating properties of the magnetic coil, this time under magnetization of three sinusoidal components. In the two-component case above it was noted that in order to have selfistarting oscillations it is necessary to have a difference combination frequency (lower side-frequency coinciding with the frequency to be generated and also that the amplitude of the generated voltage at this frequency must be proportional to the first power of amplitude of the current to be generated. The first of these is necessary in order to have 9. portion of the generated voltage opposite in phase to the voltage drop in the external resistance, and the second is necessary for self starting since it implies that the negative resistance corresponding to the generated voltage does not approach zero as the amplitude of the current becomes very small. It will be found upon substitution of the assumed magnetizing force function due to the three components into the polynomial expression for flux density that these requirements will be met only if we have combination frequencies of the form 2mf1f:=fa and 2mf1fa=f: with voltage amplitudes proportional to P1271); and P -P3 respectively. It turns out that the negative resistances in this case do not approach zero as P2 and P3 become very small. Hence the negative resistances retain the power to nullify the external resistance even when P: and P3 are very small. Experiment verifies the obvious conclusion that in obtaining these oscillations m=l is the most favorable value since third order modulation products are used and these give higher voltages than do the higher orders of modulatlo products.

It should be noted that no restrictions are put on the frequencies 1: and f3 other than the one given above, 1. e., 2mf1=f:+fa. Thus. f: and I: may be incommensurable with 11 or they may be rationally related. Any two frequencies satisfying this relation can be established, the oscillations being self-starting so long as the cricuit is within the range of conditions specified above. Furthermore, having been established they will then be maintained over a finite range of reactance and resistance variation.

In the description which has been given thus far no definite specification has been given as to the nature of the impedance Z other than that taken with La it shall in the two-component case have one degree of freedom and in the threecomponent case have two degrees of freedom. A number of circuits which are appropriate in the latter case are shown in Figs. to 13. Each of these circuits has two degrees of freedom, 1. e., in combination with the inductance. Lo may be tuned to two frequencies f: and is. The arrangement of Figs. 14 and 15 although not equivalent to the other four may be used satisfactorily since be modified by the insertion of the resonance at two frequencies 1: and I: in the loop of L0 may be maintained when the presence of L0 is taken into account; The resistance load may be added in series with any of these networks. For the circuits of Figs. 10 to 13 a resistance may be included in each branch to provide a separate load at each frequency. If only one of the components is desired as output a selective filtering circuit containing the load may be connected across a part or all of the network.

For these circuits also it is desirable to have an anti-resonance at ii to prevent Z from shunting L0 to an appreciable extent at h. The need for an anti-resonance at i1 may be avoided by using two balanced magnetic cores connected oppositely with respect to the applied wave so that ii is balanced out of the winding connected to Z.

In all of these arrangements'the circuits are not perfectly selective and other components besides those having frequencies h, ]z and in will iiow. If f1, f2 and is are rationally related then the other components will be additional terms in a Fourier series, whose fundamental term has a frequency which is the greatest common divisor of f1, f2 and is. If two of the frequencies f1, f2 and f3 are incommensurable the other compo nents will be additional terms in a double Fourier series. The flow of these components produces various effects and particularly if the term with the upper side frequency 2f1+fz flows, it will absorb energy from the generated component of frequency f: and so reduce the value of R2rn, l. e., it introduces a positive resistance instead of a negative one. But analysis shows further that the flow of this component 213+ will also introduce negative resistances at other frequencies because of higher order modulation products. For example, its flow will introduce a negative resistance at f3 due to fifth order modulation. The circuits in which the air inductances can be made as large as is convenient will be more selective than those in which this inductance has a fixed relation to L0. The circuits of Figs. 10 to 13 are of the former type while those of Fig. 14 are of the latter. The fiow of the additional components in small quantities does not invalidate the analysis given above or the conclusions therefrom.

Other forms of circuit may be used to specify the condition for self-starting although not usually in the most favorable manner. Fig. 16 shows one of these in which 2 is a resonant circuit with fairly high impedance tuned in series with the effective value of L0 at 72. No tuning coil is used in the input so that this mesh is partially tuned at both f1 and f: or at least so adjusted that the starting conditions are satisfied. Such a circuit, for example, was set up to generate a one-third subfrequency, i. e., 1::1/3 l1 and fz=5/3 f1. These frequencies were found present in the two portions of the circuit. When a simple anti-resonance at fa was connected in series with the condenser C1 then oscillations would not arise'but would start only upon removal of the anti-resonance 0r sufllcient detuning of it to either side of is. This circuit may an inductance in series with C1 to tune this branch of the circuit o is.

Fig. 17 shows one particular application of the circuit of Fig. 16. A base frequency of 60 kilocycles was impressed on the non-linear coil L'o, the associated circuits of which were adjusted to give the subharmonic 1/3 h. The output at this frequency across a condenser was then impressed on the input of an amplifier thus supplying 20-kilocycle current to the non-linear coil L"o. The circuits associated therewith,

which are of the same form as that of Fig. 16,

i a considerable range of variations is readily obtained so long as one can get within the range given by the limitations already set forth. Thus a form of Z network given in Fig. 14 was used in the circuit of Fig. l and variations from 15 to microfarads was allowable in the series condenser C14 and from to volts in the generator voltage E1 and the derived frequency remained constant throughout such variations,

It may be noted in this connection that if the reactance at is in the circuit of Fig. 16 is detuned fromzero sufhciently by adding a large inductance in series in the input mesh, we approach the form of circuit required for the twocomponent case and so this latter is a special case of the more general one. A better idea is obtained of what happens as the change is made from one case to the other by observing the changes that occur in the amplitude resistance curve of Fig. 8. Suppose this curve is'Pz plotted against R2 and that the reactance at is is being detuned from zero. Then according to the condition for starting given in Equation 2 the intersection point R20 of the curve moves to the left as the detuning from zero increases. Ultimately R20 will become zero and the curve will have changed into one like those of Fig. 3.

In the analysis, as given above, a single valued magnetic characteristic was assumed. Hence the results do not take into account explicitly the losses which occur in the magnetic core. It is to be understood, however, that such losses are reflected in the windings as an equivalent resistance and such resistance is to be understood as being included in and as being a part ofthe external resistances as considered above.

What is claimed is:

1. In a circuit for generating a non-harmonic component of a base frequency f1 comprising a non-linear inductance, an input circuit including a source of sinusoidal waves of said base frequency connected across said inductance, and an output circuit for the generated frequency connected across said inductance, means to make said generating circuit self-starting and selfsustaining for the generated non-harmonic frequency component comprising an impedance network in said output circuit making the reactances X2 and Ya of said output circuit at the frequencies f: and f3, respectively, such as to substantially neutralize the reactance X2 and X3 of said inductance at these respective frequencies, and making the total resistance R2 and R3 of said output circuit and said inductance at these respective frequencies less than a critical value R2111 which is a function of the effective reactance of said inductance, as defined in the specification, one of the two frequencies f2 and f3 being the non-harmonic frequency component to be gen-- erated and the two frequencies being related to the base frequency f1 by the relation 2mf1=fz+fi where m is an integer.

,2. The combination of claim 1, in which said critical value of resistance is determined by the relation RzRa- XQXa.

3. A circuit for obtaining a non-harmonic component of a base frequency f1 comprising a nonlinear inductance, a source of sinusoidal waves of said base frequency, an input circuit connecting said source across said non linear inductance and an output circuit for the generated frequency connected across said inductance, said output circuit as a whole having two degrees of freedom at the frequencies f2 and fa, respectively, one of which is the frequency Ofthe non-harmonic component to be generated and which are related to said base frequency in accordance with the equation 2mf1=f2+f3 where m is an integer, the total impedances Z and Z: of said output circuit with said inductance at the frequencies f: and f3, respectively, being reduced to substantially a minimum and coming within the relation zzza xi'xa', where X2 and K1 are the reactances of said inductance at the frequencies f2 and 13, respectively. I

4. The combination of claim 3 in which said non-linear impedance is a saturable magnetic core coil and said output circuit comprises at least two parallel impedance branches tuned with said coil to provide said two degrees of freedom.

5. The combination of claim 3 in which said non-linear inductance is a saturable magnetic core coil and said output circuit comprises two parallel branches each containing linearinductance and, capacitance in series, one of said branches being tuned with said coil to the frequency f2 and the other being tuned with said coil to the frequency is.

- 6. A self-starting even harmonic generator for generating a harmonic of frequency f2 and amplitude P2 from a base frequency f1, comprising an unbiased saturable magnetic core coil, a sinusoidal voltage source of frequency 11 and amplitude P1 for exciting said coil, and an output circuit for the generated harmonic, connected in parallel with said exciting voltage source, across said coil, said output circuit having a reactance such as to approximately neutralize the reactance of said coil at the frequency f for the particular values of P1 and P2 involved, the combined resistance of said output circuit and said coil being less than a critical value R2111 which is a function of the effective inductance of said coil.

JACK M. MANLEY. 

